We study one- and two-photon scattering from a qubit embedded in a one-dimensional waveguide in the presence of modal dispersion. We use a resolvent based analysis and utilize techniques borrowed from the Lee model studies. Modal dispersion leads to atom-photon bound states which necessitate the use of multichannel scattering theory. We present multichannel scattering matrix elements in terms of the solution of a Fredholm integral equation of the second kind. Through the use of the Lippmann-Schwinger equation, we derive an infinite series of Feynman diagrams that represent the solution to the integral equation. We use the Feynman diagrams as vertex correction terms to come up with closed-form formulas that successfully predict the trapping rate of a photon in the atom-photon bound state. We verify our formalism through Krylov-subspace based numerical studies with pulsed excitations. Our results provide the tools to calculate the complex correlations between scattered photons in a dispersive environment.

We report state-resolved electron-momentum correlation measurement of strong-field nonsequential double ionization in benzene. With a novel coincidence detection apparatus, highly efficient triple coincidence (electron-electron dication) and quadruple coincidence (electron-electron-cation-cation) are used to resolve the final ionic states and to characterize three-dimensional (3D) electron-momentum correlation. The primary states associated with dissociative and nondissociative dications are assigned. A 3D momentum anticorrelation is observed for the electrons in coincidence with dissociative benzene dication states whereas such a correlation is absent for nondissociative dication states.

Motivated by experiments in Munich [M. Schreiber et al., Science 349, 842 (2015).], we study the dynamics of interacting fermions initially prepared in charge density wave states in one-dimensional bichromatic optical lattices. The experiment sees a marked lack of thermalization, which has been taken as evidence for an interacting generalization of Anderson localization, dubbed “many-body localization.” We model the experiments using an interacting Aubry-Andre model and develop a computationally efficient low-density cluster expansion to calculate the even-odd density imbalance as a function of interaction strength and potential strength. Our calculations agree with the experimental results and shed light on the phenomena. We also explore a two-dimensional generalization. The cluster expansion method we develop should have broad applicability to similar problems in nonequilibrium quantum physics.

We suggest a method for accurate parameter estimation of atomic systems, employing the special properties of the exceptional points. The non-Hermitian degeneracies at the exceptional points emerge from the description of the spontaneous emission of the atomic system in the framework of an open quantum system, resulting in a non-Hermitian quantum master equation. The method is demonstrated for the atomic spectrum of $S\to P$ transitions of ${}^{85}\mathrm{Rb}$ and ${}^{40}\mathrm{Ca}^{+}$.

We construct triqubit genuinely entangled states which have positive partial transposes (PPTs) with respect to the bipartition of systems. These examples disprove a conjecture [Novo, Moroder, and Gühne, Phys. Rev A 88, 012305 (2013)] which claims that PPT mixtures are necessary and sufficient for the biseparability of three qubits.

Guaranteeing nonrepudiation, unforgeability as well as transferability of a signature is one of the most vital safeguards in today's e-commerce era. Based on fundamental laws of quantum physics, quantum digital signature (QDS) aims to provide information-theoretic security for this cryptographic task. However, up to date, the previously proposed QDS protocols are impractical due to various challenging problems and most importantly, the requirement of authenticated (secure) quantum channels between participants. Here, we present the first quantum digital signature protocol that removes the assumption of authenticated quantum channels while remaining secure against the collective attacks. Besides, our QDS protocol can be practically implemented over more than 100 km under current mature technology as used in quantum key distribution.

We propose an entanglement purification scheme based on material qubits and ancillary coherent multiphoton states. We consider a typical QED scenario where material qubits implemented by two-level atoms fly sequentially through a cavity and interact resonantly with a single mode of the radiation field. We explore the theoretical possibilities of realizing a high-fidelity two-qubit quantum operation necessary for the purification protocol with the help of a postselective balanced homodyne photodetection. We demonstrate that the obtained probabilistic quantum operation can be used as a bilateral operation in the proposed purification scheme. It is shown that the probabilistic nature of this quantum operation is counterbalanced in the last step of the scheme where qubits are not discarded after inadequate qubit measurements. As this protocol requires present-day experimental setups and generates high-fidelity entangled pairs with high repetition rates, it may offer interesting perspectives for applications in quantum information theory.

We consider the decomposition of arbitrary isometries into a sequence of single-qubit and controlled-not (cnot) gates. In many experimental architectures, the cnot gate is relatively costly and hence we aim to keep the number of these as low as possible. We derive a theoretical lower bound on the number of cnot gates required to decompose an arbitrary isometry from $m$ to $n$ qubits and give three explicit gate decompositions that achieve this bound up to a factor of about 2 in the leading order. We also perform some further optimizations for certain cases where $m$ and $n$ are small. In addition, we show how to apply our result for isometries to give a decomposition scheme for an arbitrary quantum operation via Stinespring's theorem and derive a lower bound on the number of cnot gates in this case too. These results will have an impact on experimental efforts to build a quantum computer, enabling them to go further with the same resources.

NMR shielding constants for He- and Be-like atomic systems of Ne, Ar, Kr, Xe, and Rn have been calculated at the random-phase-approximation level of approach, including an estimation of QED corrections within the polarization propagator formalism. We show that QED effects enhance electron correlation when $Z$ becomes heavier, which happens with relativistic effects, and also that QED effects become smaller when going from more to less ionized systems. We studied two- and four-electron systems. Then such studies could easily be generalized to other many-electron systems. Results of calculations with our relatively simple model, which includes QED and electron correlation effects on the same theoretical grounds, have a summarized error in the range from 10% (for Ne) up to 24% (for Rn), so that our accuracy is a little lower than for calculations on H-like systems. Our findings should stimulate the development and/or the application of more rigorous formalisms to get more accurate QED corrections to response properties in many-electron systems.

We theoretically and numerically study spin wave turbulence in spin-1 ferromagnetic spinor Bose-Einstein condensates, finding direct and inverse cascades with power-law behavior. To derive these power exponents analytically, the conventional weak wave turbulence theory is applied to the spin-1 spinor Gross-Pitaevskii equation. Thus we obtain the $-7/3$ and $-5/3$ power laws in the transverse spin correlation function for the direct and inverse cascades, respectively. To confirm these power laws, numerical calculations are performed that obtain results consistent with these power laws.

Soliton evolution at diffusive Kerr-type media is analyzed within the framework of the Helmholtz theory. The angular limitations of previous paraxial studies are overcome when both soliton propagation and diffusion of carriers are allowed to occur along any arbitrary direction. A model including two-dimensional carrier diffusion is proposed and its exact soliton solutions within the weakly nonlocal regime are presented. The restriction of carrier diffusion to a single transverse coordinate leads to the breakdown of the rotational symmetry of the Helmholtz framework and soliton behavior becomes angular dependent. We study the impact of this limitation in an intrinsic angular scenario, such as a nonlinear interface.

We present an exact rewriting of the Mie coefficients describing the scattering of light by a spherical core-shell particle which enables their interpretation in terms of a hybridization of the two surface modes arising, respectively, at the core-shell and the shell-medium interface. For this particular case, we thus obtain from the Mie theory—analytically for all multipole orders and hence for arbitrarily sized particles—the hybridization scenario, which so far has been employed primarily for small particles in the electrostatic approximation. To demonstrate the strength of the rewriting approach, we also extract the hybridization scenario for a stratified sphere directly from the expansion coefficients for the electromagnetic fields.

Experimental violations of Bell inequalities are in general vulnerable to so-called loopholes. In this work, we analyze the characteristics of a loophole-free Bell test with photons, closing simultaneously the locality, freedom-of-choice, fair-sampling (i.e., detection), coincidence-time, and memory loopholes. We pay special attention to the effect of excess predictability in the setting choices due to nonideal random-number generators. We discuss necessary adaptations of the Clauser-Horne and Eberhard inequality when using such imperfect devices and—using Hoeffding's inequality and Doob's optional stopping theorem—the statistical analysis in such Bell tests.

Physically valid and numerically efficient approximations for the exchange and correlation energy are critical for reduced-density-matrix-functional theory to become a widely used method in electronic structure calculations. Here we examine the physical limits of power functionals of the form $f(n,n^{\prime })={\left(n{n}^{\prime }\right)}^{\alpha }$ for the scaling function in the exchange-correlation energy. To this end we obtain numerically the minimizing momentum distributions for the three- and two-dimensional homogeneous electron gas, respectively. In particular, we examine the limiting values for the power $\alpha$ to yield physically sound solutions that satisfy the Lieb-Oxford lower bound for the exchange-correlation energy and exclude pinned states with the condition $n\left(\mathbf{k}\right)<1$ for all wave vectors $\mathbf{k}$. The results refine the constraints previously obtained from trial momentum distributions. We also compute the values for $\alpha$ that yield the exact correlation energy and its kinetic part for both the three- and two-dimensional electron gas. In both systems, narrow regimes of validity and accuracy are found at $\alpha \gtrsim 0.6$ and at $r_s\gtrsim 10$ for the density parameter, corresponding to relatively low densities.

Thermal electron attachment rate coefficients for three interhalogen compounds (ClF, ICl, IBr) have been measured from 300 to 900 K at pressures of 1–2 Torr using a flowing afterglow–Langmuir probe apparatus. ClF attaches somewhat inefficiently ($k=7.5\times {10}^{-9}\mathrm{c}{\mathrm{m}}^3{\mathrm{s}}^{-1}$) at 300 K, with the rate coefficient rising to $1.7\times {10}^{-8}\mathrm{c}{\mathrm{m}}^3{\mathrm{s}}^{-1}$ at 700 K. At higher temperatures the apparent rate coefficient falls steeply; however, this is interpreted as an artifact due to decomposition on the walls of the inlet line. ICl attaches with even lower efficiency ($k=9.5\times {10}^{-10}\mathrm{c}{\mathrm{m}}^3{\mathrm{s}}^{-1}$ at 300 K) and a less steep increase with temperature. Attachment to IBr is too slow to confidently measure with the present experiment, with an upper limit on the rate coefficient of ${10}^{-10}\mathrm{c}{\mathrm{m}}^3{\mathrm{s}}^{-1}$ from 300 to 600 K. Both ClF and ICl attach dissociatively to yield $\mathrm{C}{\mathrm{l}}^{-}$, likely exclusively, though ${\mathrm{F}}^{-}$ or ${\mathrm{I}}^{-}$ may be produced with limits of $<2\%$ and $<5\%$, respectively. The ClF attachment was further explored through ab initio calculation of the ClF and $\mathrm{Cl}{\mathrm{F}}^{-}$ potential energy curves and $R$-matrix calculations of the resonance parameters which were used then for calculations of the dissociative attachment cross sections and rate coefficients. While the magnitude of the attachment rate coefficient for ClF is similar to those for both $\mathrm{C}{\mathrm{l}}_2$ and ${\mathrm{F}}_2$, the calculated cross sections show qualitatively different threshold behavior due to the $s$-wave contribution allowed by the lack of inversion symmetry. The $v=1$ and 2 vibrational modes of ClF attach about three to four times faster than $v=0$ and 3 at energies lower than $\sim 0.2\mathrm{eV}$. The calculated rate coefficients are in good agreement with the experiment at 300 K and increase moderately less steeply with temperature.

We study the quasistability of UV-pulse-train-excited H atoms in a strong infrared (IR) laser as a function of the phase delay of the UV pulse train relative to the IR laser. The UV pulse train contains two frequency components. When the two components have frequencies separated by two IR photons, the population of surviving electrons is modulated by up to ten percent. When electrons are excited to right above or below the threshold, the survival probabilities have inverted phase delay dependence, which can be explained classically. When the two frequencies are one IR photon apart, the angular symmetry of the quasistable electrons is broken, and the asymmetry is also controlled by the phase delay. The asymmetrical distribution can be observed while the IR is on and smoothly evolves to a nonzero asymmetry that only weakly depends on the duration of the IR field.

It was recently shown [J. C. Halimeh et al., Phys. Rev. A 93, 013850 (2016)] that as a result of the Doppler effect, inherently dispersive single-frequency ideal free-space invisibility cloaks in relative motion to an observer can only cloak light whose frequency in the cloak frame coincides with the operational frequency of the cloak, although an infinite number of such rays exist for any cloak motion. In this article, we show analytically and through ray-tracing simulations that even though this relationship can be relaxed by simplifying the ideal invisibility cloak into a broadband amplitude cloak, Fresnel-Fizeau drag uncloaks the phase of light in the inertial frame of the cloak thereby compromising its amplitude cloaking in all other inertial frames. In other words, only an invisibility device that perfectly cloaks both the amplitude and the phase of light in its own inertial frame will also (perfectly) cloak this light in any other inertial frame. The same conclusion lends itself to invisible objects that are not cloaks, such as the invisible sphere.

The dynamical behavior of Kerr optical frequency combs is very well understood today from the perspective of the semiclassical approximation. These combs are obtained by pumping an ultrahigh-$Q$ whispering-gallery mode resonator with a continuous-wave laser. The long-lifetime photons are trapped within the toruslike eigenmodes of the resonator, where they interact nonlinearly via the Kerr effect. In this article, we use quantum Langevin equations to provide a theoretical understanding of the nonclassical behavior of these combs when pumped below and above threshold. In the configuration where the system is under threshold, the pump field is the unique oscillating mode inside the resonator, and it triggers the phenomenon of spontaneous four-wave mixing, where two photons from the pump are symmetrically up- and down-converted in the Fourier domain. This phenomenon, also referred to as parametric fluorescence, can only be understood and analyzed from a fully quantum perspective as a consequence of the coupling between the field of the central (pumped) mode and the vacuum fluctuations of the various side modes. We analytically calculate the power spectra of the spontaneous emission noise, and we show that these spectra can be either single- or double-peaked depending on the value of the laser frequency, chromatic dispersion, pump power, and spectral distance between the central mode and the side mode of interest. We also calculate as well the overall spontaneous noise power per side mode and propose simplified analytical expressions for some particular cases. In the configuration where the system is pumped above threshold, we investigate the phenomena of quantum correlations and multimode squeezed states of light that can occur in the Kerr frequency combs originating from stimulated four-wave mixing. We show that for all stationary spatiotemporal patterns, the side modes that are symmetrical relative to the pumped mode in the frequency domain display quantum correlations that can lead to squeezed states of light under some optimal conditions that are analytically determined. These quantum correlations can persist regardless the dynamical state of the system (rolls or solitons), regardless of the spectral extension of the comb (number side modes) and regardless of the dispersion regime (normal or anomalous). We also explicitly determine the phase quadratures leading to photon entanglement and analytically calculate their quantum-noise spectra. For both the below- and above-threshold cases, we study with particular emphasis the two principal architectures for Kerr comb generation, namely the add-through and add-drop configurations. It is found that regardless of the configuration, an essential parameter is the ratio between out-coupling and total losses, which plays a key role as it directly determines the efficiency of the detected fluorescence or squeezing spectra. We finally discuss the relevance of Kerr combs for quantum information systems at optical telecommunication wavelengths below and above threshold.

To provide a detailed description of the dynamics of laser beam propagation in the atmosphere we use the method of the photon distribution function in the phase space, which reduces the analysis to consideration of photon trajectories and their correlations. The scintillation index ${\sigma }^2$ is calculated for the range of moderate and strong turbulence, which is the most challenging for analytical consideration. The considerable growth of ${\sigma }^2$ (by two to three times) found for moderate turbulence is shown to be due to correlations between photon trajectories. Our calculations demonstrate that the maximum of ${\sigma }^2$ can be considerably decreased by an increase of the source aperture or the use of the fast phase diffuser.